4. [Extra credit: 10 points] An algebraic number is the solution of a univariate polynomial equation p(x) = 0, where p has integer coefficients. (So, for example, 2 is algebraic, since it is the solution to the equation u3-2 20.) Prove that the algebraic numbers are countable. Hint: Use the following facts, which I am not asking you to prove: If X is a countable set, then X is countable. (This isn't that hard to prove, but I don't want to distract you from the main task at hand.) A polynomial of degree n having complex coefficients has n complex roots, allowing for multiple roots. (This is called thefundamental theorem of algebra, which you are encouraged to read about in your copious spare time.)